Just to confuse you, you give hypertonic saline with furosemide to get rid of free water in hyponatremia due to SIADH (except in patients with high volume status like edematous cirrhosis, CHF, or RF where you avoid giving Na and restrict free water intake).
You can give furosemide because it blocks the countercurrent exchange required for ADH to reabsorb water in the collecting duct. However, thiazides are actually a common cause of hyponatremia because ADH can still function and UNa>SNa.
By the way, you give furosemide in people with edema. You don't generally give thiazides because they already trend to be hyponatremic due to edema despite having higher total body sodium. You give thiazides to hypertensives as a first line because it has activity on the vasculature also besides its function in the tubules.
